The discovery of gravitational wave signals from merging black holes and neutron stars [1]} has
been a recent milestone for general relativity and astrophysics. The different present and planned
gravitational wave detectors are reaching higher and higher sensitivity [2]}, which requires
more detailed predictions on the theoretical side than currently available. The motion of gravitating
massive binary systems was studied perturbatively expanding in higher post–Newtonian (PN) orders right
after the theory of general relativity has been found [3]}, [4]}. Later on the corrections at
2 PN [5]}, 3 PN [6]} and 4 PN [7]}, PN,Foffa:2019rdf,Foffa:2019yfl,
Blumlein:2020pog
have been calculated using a variety of techniques. First results at 5 PN have been
obtained in Refs. [8]}, [9]}, [10]}, [11]}, [12]}, [13]} and
at 6 PN in Refs. [14]}, [15]}, [16]}.There is also a lot of activity in
calculating post–Minkowskian corrections, cf. [14]}, Ref. [12], and
[18]}, [19]}, [20]}, [21]}.
In the Schwarzschild limit the contributions of \(O(\nu ^0)\)  are obtained to all post–Newtonian orders and the terms
of \(O(\nu )\)  are know to \(O(G_N^{21.5})\)  [22]}, [23]} from the self–force formalism
[24]}Also in self–force calculations regularizations are applied. In the present paper we are not
discussing this aspect, but assume that the final results derived are regularization–independent.,
where \(G_N\)  denotes Newton's constant. The following kinematic variables are used
\(\nu = \frac{m_1 m_2}{M^2} \in \left[0,\tfrac{1}{4}\right],~~~M = m_1 + m_2,~~~m_{1,2} = \frac{1}{2} M\left[1 \pm \sqrt{1 - 4 \nu }\right],~~\mu = M \nu ,\) 
